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How do you find f'(1) if #f(x)= x^2*tan^-1 x#?

Answer 1

William Abdalla

It would be #pi/2+1/2#

f' (x)= #2x tan^-1 x + x^2 /(1+x^2)#

f' (1)= # 2tan^-1 1+ 1/2#

=#2pi/4 +1/2#

=#pi/2 +1/2#

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Answer 2

Paisley Johnson

To find ( f'(1) ) if ( f(x) = x^2 \tan^{-1}(x) ), use the product rule and the chain rule.

( f'(x) = 2x \tan^{-1}(x) + \frac{x^2}{1+x^2} )

Evaluate ( f'(1) ) using this derivative expression.

( f'(1) = 2(1) \tan^{-1}(1) + \frac{1^2}{1+1^2} )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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